Pentagon abcde and pentagon a'b'c'd'e' are shown on the coordinate plane below: pentagon abcde and pentagon a prime b prime c prime d prime e prime on the coordinate plane with ordered pairs at a negative 4, negative 2, at b negative 6, negative 3, at c negative 5, negative 6, at d negative 2, negative 5, at e negative 2, negative 3, at a prime 3, 1, at b prime 1, 2, at c prime 2, 5, at d prime 5, 4, at e prime 5, 2 which two transformations are applied to pentagon abcde to create a'b'c'd'e'? translated according to the rule (x, y) →(x + 7, y + 1) and reflected across the x-axis translated according to the rule (x, y) →(x + 1, y + 7) and reflected across the x-axis translated according to the rule (x, y) →(x + 7, y + 1) and reflected across the y-axis translated according to the rule (x, y) →(x + 1, y + 7) and reflected across the y-axis

Translated according to the rule (x, y) →(x + 7, y + 1) and reflected across the x-axis

Step-by-step explanation:

We are given Pentagon ABCDE.

with vertices as:

A (-4,-2) , at B(-6,-3) at C (-5,-6), at D (-2,-5) at E (-2,-3)

and the pentagon A'B'C'D'E' with vertices as:

A'(3,1) , B'(1,2) , C'(2,5) , D'(5,4) and E'(5,2).

Clearly we could observe that the image is formed by the translation and reflection of the pentagon ABCDE.

First the Pentagon is translated by the rule:

(x,y) → (x+7,y+1) so that the pentagon is shifted to the fourth coordinate  and then it is reflected across the x-axis to get the transformed figure in the first coordinate plane as Pentagon A'B'C'D'E'.

Hence, the answer is:

Translated according to the rule (x, y) →(x + 7, y + 1) and reflected across the x-axis

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.

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step-by-step explanation: